Rapid, Direct, Noninvasive Method to Determine the Amount of Immobilized Protein

Protein immobilization is of utmost importance in many areas, where various proteins are used for selective detection of target compounds. Despite the importance given to determine the amount of immobilized protein, there is no simple method that allows direct, noninvasive detection. In this work, a method based on pH transition, occurring during change of solution ionic strength, was developed. The method utilized the ionic character of the immobilized protein while implementing biologically compatible buffers. Five different proteins, namely, glucose oxidase, horseradish peroxidase, bovine serum albumin, lysozyme, and protein A, were immobilized in different amounts on a porous polymeric matrix, and their pH transition was measured using lactate buffer of various concentrations and pH values. A linear correlation was found between the amount of immobilized protein and the amplitude of the pH transition, allowing the detection down to 2 nmol of immobilized protein. By changing the buffer concentration and pH, the sensitivity of the method could be tailored. Criteria based on the symmetry of the pH transition peak have been developed to determine if a particular measurement is within a linear range. In addition, a mathematical model was developed enabling prediction of pH transition profiles based solely on the protein amino acid sequence, the buffer pKa value(s), and the amount of immobilized protein.Hence, it can be used to design pH transition method experiments to achieve the required sensitivity for a target sample. Since the proposed method is noninvasive, it can be routinely applied during optimization of the immobilization protocol, for quality control, and also as an in-process monitoring tool.


Table of content
 The developed framework for proposed mathematical model.
S-2  Calculations and solution routine S-5  Effect of covalent biding and denaturation on pH profile S-7  Solution algorithm and limit of detection S-9  Figure S1: Schematic diagram of the pH transition measurement.
S-5  Figure S2: Effect of number of lysine residue on the pH transition profiles for samples containing immobilized LYZ and protA. S-7  Figure S3: Effect of conformational changes of the protein pH profile.
S-8  Figure S4: The limit of detection of proposed method.
S-11  Figure S5: Robustness of the method.
S-12  Figure S6: Experimental and model-based pH transition profiles for samples containing immobilized BSA, LYZ, GOX and HRP. S-13  Figure S7: Model-based pH transition profiles as a function of immobilized masses for protA, LYZ and GOX. S-14  Figure S8: Effect of buffer composition on the linear region of protA.
S-15  Table S1: Summary of immobilized protein properties.
S-16  Table S2: The pH peak asymmetry as a function of the immobilized mass of the protein.
S-16  Table S3: The peak height and peak width ratio of tested pH peak.
S-17  References S-18 S-2 1. The developed framework for proposed mathematical model: To account for solution equilibria, the charged species must satisfy the electroneutrality condition at a given pH: where Kw is the ionic product of water, Cb i+ and Ca jare the concentrations of the charged basic and acidic buffer species, respectively, and M and N are the valence of the charged basic and acidic buffer species, respectively. The concentration of the charged buffer species can be calculated by considering the dissociation equilibrium. For an acidic buffer (as in our study) with valence Ni, the concentration of each buffer species is given by: for m = 1,2…Ni (2) where CTOT is the total buffer concentration, Ni is the ion valence, and Ka,i is the deprotonation constant for individual buffer species. Eq 2 can be adopted also for basic buffers with only minor modifications 1, 2 . Note that the activity coefficients are required to calculate the correct dissociation constants and can be determined according to the Davies equation 2 . Subsequently, eq 1-2 can be solved numerically for CH + which allows the calculation of the pH.
Two types of amino acid residues may be present on immobilized protein molecules, namely weak acid groups and weak base groups. The acid groups dissociation is described as: is an apparent dissociation constant for acidic groups and can be estimated from the residual pKa(s) (Table S1). Likewise, basic groups dissociation is described as: is an apparent dissociation constant for basic groups and can be estimated from the residual pKb(s) ( Table S1). The qi are the concentrations of protonated and deprotonated functional groups present in the respective (acidic or basic) matrix. To account for the matrix electroneutrality, the following condition must be satisfied: In practice, it turns out that both qOHand qH + are usually negligible 1, 3, 4 , while only one of qRand qRH + is relevant at certain pH values (depending on the charge distribution of the proteins).
By combining eq 3-7, we obtain a general approximation for sodium ions: and/or chloride ions: when NaCl is used to change buffer ionic strength, where q0 is the total concentration of the individual weak acid or base functional groups (residues) on the protein molecule, Ka, and Kb are the dissociation constants for acid and base residues, n is the number of groups capable of parallel dissociations (in our case typical n = 1), and K is the number of different ionic groups/residues that can be protonated. In the case studied, this is also the number of different charged residues. Finally, solution and phase equilibrium can be related by the Donnan equilibrium: where we assume that anions and cations are exchanged unrelatedly, yet highly dependent on solution and matrix pH value. For a given initial values of CH + , CCl -, CNa + and CTOT the qNa + and/or qClcan be calculated using eq 1-11. Note that q0 is directly related to the concentration of the immobilized protein, while Ka and n are determined by the nature of the immobilized protein via its amino acid sequence. S-5

Calculations and solution routine
Since the pH transition is a dynamic phenomenon, it was studied in a flow-through mode ( Figure S1). Furthermore, a porous matrix was considered for protein immobilization, as being frequently used to increase the specific surface area, resulting in a higher amount of immobilized protein and thus a higher conversion or binding capacity. Due to an open-pore structure and flow regime, the material balance model describing the plug flow was used to predict the dynamics of the individual component: where z is the axial coordinate of the matrix, u is the superficial velocity, ε is the open matrix porosity, and Di is the axial dispersion coefficient. For the non-retained components, such as buffers, = and local equilibrium is assumed, while for retained components, such as sodium and chloride ions, = + (1 − ) , and can be calculated based on eq 8-11.

S-6
A numerical solution of the conservation equations (12) was obtained by discretizing the axial derivative using forward finite differences and solving the resulting set of ordinary differential equations in time with built-in solvers in the MATLAB library. Numerical dispersion caused by the discretization was minimized by increasing the number of discretization points. All calculations were performed in MATLAB R2016b on a regular PC, with all results obtained within minutes. S-7

Effect of covalent biding and denaturation on pH profile
Initially the simulations in which one of the lysine residues was omitted, assuming that it reacted with the matrix during immobilization (which is a commonly applied mechanism), was performed to check the effect of covalent biding on pH profile. No obvious difference was observed in the protA simulation, whereas only a slight deviation was observed in the LYZ simulation ( Figure S2). This can be attributed to the fact that LYZ has a smaller number of charged residues per molecule, implying that the relative contribution of a single amino acid residue is higher. Nevertheless, the insignificant difference suggests that the original protein amino acid sequence available in the database can be used to predict the pH shifts of the immobilized protein. In addition, protein denaturation tests were performed to evaluate possible effects of conformational changes on pH profiles. A standard procedure with urea solution was performed 5 (samples without and with 0.979 mg immobilized protein A were transferred into 8 M urea for 1h at 60°C) and the pH profiles were evaluated before and after exposure. Since no obvious difference was observed (Fig. S3), we can conclude that protein denaturation does not affect the pH transition profile.

Solution algorithm and limit of detection
A simple algorithm was developed that allows accurate experimental determination of the amount of immobilized protein and can be summarized as follows: i) the pH transition method is applied to a blank matrix (without immobilized protein), as it may also have some ionic character; ii) the blank matrix is immobilized with a selected protein and its amount is accurately determined by suitable non-destructive measurement (some of which are described in the Introduction section); iii) the pH transition method is then applied to a selected buffer-immobilized protein system, and the blank response from step i) is subtracted from the obtained pH shift; iv) the pH peak is evaluated based on its asymmetry -if the ratio between pH peak height and width, determined at 90% height, is below 4, a linear correlation between the pH peak height and the immobilized mass is expected. Otherwise, the buffer pH should be adjusted and steps i) and iii) repeated until the proposed criterion is met; v) once the measurement falls within the linear range, the sensitivity and duration of the method can be adjusted by changing the buffer concentration (e.g., lowering the buffer concentration to increase sensitivity); vi) when all of the above points are considered, the two-point linear correlation can be constructed using the measured point and the origin point (similar to Figure 2H). This correlation can then be used to determine the amount of immobilized protein.
This approach is similar to the two-point calibration commonly performed prior to measurements with any sensor. Although the mathematical model allows for in-silico S-10 prediction of the pH transition, the potential effect of the matrix itself cannot be considered and should therefore be determined experimentally on a case-by-case basis. Therefore, this method allows a simple, direct and non-invasive determination of immobilized protein amount using biological buffers. Their concentration and pH affect the sensitivity and linear range of the method and are therefore a powerful tool to adjust conditions to a particular immobilized protein and its amount. While we are flexible with buffer adjustment to increase method sensitivity, there is lower limit of detection determined by exceedingly low buffer capacity required to detect extremely small quantities of immobilized protein, disabling method robustness and therefore reproducibility. Another challenge to the application of the method is that the immobilization matrix is charged since it significantly affects the shape of the pH transition profile. Although the pH transition profile of the original immobilization matrix (matrix prior to protein immobilization) is always measured and subtracted from the final pH transition signal, the accuracy of protein estimation is lower when the contribution of the matrix is comparable or even larger than that of the protein itself. The best accuracy of commercially available pH electrodes is in the range of 0.01-0.05 pH units 6 . Assuming a change of 0.05 pH units as the limit of quantification, one can determine a mass of about 50 µg of immobilized protein (corresponding to less than 2 nanomoles for protA), as demonstrated in Figure S4. The application of the proposed method is further facilitated by a developed mathematical model that accurately predicts the direction and magnitude of the pH shift. Its greatest strength is that it requires only protein amino acid sequence and buffer pKa value(s). However, since many proteins can contain tags to facilitate their purification (e.g. 6xHis or GST) 7, 8 , they should be also considered in a mathematical model calculation to correctly predict the pH transition profile. Still, proposed model is a powerful tool for in-silico design of pH measurements to adjust buffer conditions for required pH response and to establish conditions for a broad linear response range. Needless to say, due to its simplicity, all results can be obtained and analyzed S-11 within a few minutes on a common PC, which is significantly faster compared to any laboratory experiment, not to mention the experimental costs.